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How many ways can a student schedule 3 mathematics courses -- algebra,

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Bunuel
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How many ways can a student schedule 3 mathematics courses -- algebra, [#permalink] New post   13 May 2019, 01:58
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How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)

A. 3
B. 6
C. 12
D. 18
E. 24
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E
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Re: How many ways can a student schedule 3 mathematics courses -- algebra, [#permalink] New post   13 May 2019, 03:02
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Bunuel wrote:
How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)

A. 3
B. 6
C. 12
D. 18
E. 24


total ways
three subjects can be arranged in 6 periods such that no two come in consective ; 4 ways
and three subjects can be arranged in 3! ways ; 6
so total possiblities; 4* 6; 24
IMO E
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nick1816
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Re: How many ways can a student schedule 3 mathematics courses -- algebra, [#permalink] New post   13 May 2019, 03:34
a M b M c M d
a≥0, b≥1, c≥1 and d≥0
a+b+c+d=3
There are 4 solutions possible.

Total arrangements possible=4*3!=24
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KarishmaB
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Re: How many ways can a student schedule 3 mathematics courses -- algebra, [#permalink] New post   13 May 2019, 05:54
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Bunuel wrote:
How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)

A. 3
B. 6
C. 12
D. 18
E. 24


There are 3 distinct math courses and 3 other courses say X each. Place the Xs first.

X X X

Now there are 4 spots for math courses: s X s X s X s
We can pick any 3 of the 4 spots and place math courses there in 4C3 = 4 ways.
Now the three math courses can be arranged in 3! ways in the chosen 3 spots.

Number of ways = 4*3! = 24

Answer (E)
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Re: How many ways can a student schedule 3 mathematics courses -- algebra, [#permalink] New post   14 May 2019, 19:52
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Bunuel wrote:
How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)

A. 3
B. 6
C. 12
D. 18
E. 24


Letting M denote a mathematics course and X denote a non-mathematics course, we see that we can have the following schedules if no two mathematics course are to be consecutive: MXMXMX, XMXMXM, MXXMXM and MXMMXM.

Note that the three mathematics courses can be ordered in 3! = 6 ways. Further, since the courses can run in any of the 4 schedules above, there are 6 x 4 = 24 total ways in which no two mathematics courses are taken consecutively.

Answer: E
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Re: How many ways can a student schedule 3 mathematics courses -- algebra, [#permalink] New post   15 May 2019, 04:02
ScottTargetTestPrep wrote:
Bunuel wrote:
How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)

A. 3
B. 6
C. 12
D. 18
E. 24


Letting M denote a mathematics course and X denote a non-mathematics course, we see that we can have the following schedules if no two mathematics course are to be consecutive: MXMXMX, XMXMXM, MXXMXM and MXMMXM.

Note that the three mathematics courses can be ordered in 3! = 6 ways. Further, since the courses can run in any of the 4 schedules above, there are 6 x 4 = 24 total ways in which no two mathematics courses are taken consecutively.

Answer: E



Hello scott ,
Thanks for the explanation but doesnt MXMMXM takes 2 maths courses consecutively , or am i lacking in my understanding , can you please help clarify this ?

regards !
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Re: How many ways can a student schedule 3 mathematics courses -- algebra, [#permalink] New post   15 May 2019, 04:36
1st period can be any of algebra, geometry or number theory which can occupy any of the 6 periods. Hence this can be done in 6*3 =18ways.
Hence 18 cannot be the answer . Option E is only option more than 18 so can go ahead with 24 ways !

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Re: How many ways can a student schedule 3 mathematics courses -- algebra, [#permalink] New post   20 May 2019, 18:56
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ritika50 wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:
How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)

A. 3
B. 6
C. 12
D. 18
E. 24


Letting M denote a mathematics course and X denote a non-mathematics course, we see that we can have the following schedules if no two mathematics course are to be consecutive: MXMXMX, XMXMXM, MXXMXM and MXMMXM.

Note that the three mathematics courses can be ordered in 3! = 6 ways. Further, since the courses can run in any of the 4 schedules above, there are 6 x 4 = 24 total ways in which no two mathematics courses are taken consecutively.

Answer: E



Hello scott ,
Thanks for the explanation but doesnt MXMMXM takes 2 maths courses consecutively , or am i lacking in my understanding , can you please help clarify this ?

regards !


It’s a simple typo, it should have been MXMXXM instead of MXMMXM. Notice that if we have a valid schedule, we can run the same schedule in reverse direction and obtain another valid schedule (such as MXMXMX in reverse is XMXMXM). So, we simply have the reverse of MXXMXM, which is MXMXXM.
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Re: How many ways can a student schedule 3 mathematics courses -- algebra, [#permalink] New post   03 May 2024, 04:03
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